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= Homework: Section 13.4 Question 2, Instructor-c... HW Score: 29.77%, 1.79 of 6 points Points: 0.06 of 1 Sav Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 17+ 35+ 53 + . . . + (18n -1) =n(9n +8) What is the first step in an induction proof? O A. Show that the statement is true for n = k. O B. Show that the statement is true for n = 0. O C. Show that the statement is true for n = k + 1. O D. Show that the statement is true for n = 1. Complete the steps to show that the statement is true for n = 1. 17 +35 + 53 + . . . + (18n -1) = n(9n + 8) (18 . -1) ? (9.+8) 0:0 Simplify both sides. Thus, the statement is true for n = 1. What is the next step in an induction proof? O A. Assume that the statement is true for k = 1, and show that the statement must also be true for k = 2. O B. Assume the statement is true for some k, and show that the statement must also be true for the next natural number, k + 1 O C. Show that the statement is true for some k. O D. Show that the statement is true for any number k + 1. Ask my instructor Print Media Clear all Check ans DEC 5 .... WHomework: Section 13.4 Question 2, Instructor-c... HW Score: 29.77%, 1.79 of 6 points Points: 0.06 of 1 Save Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 17 + 35 + 53 + . . . + (18n -1) = n(9n +8) Assume the statement is true for some k. Complete the steps below to show that the statement must also be true for k + 1. Do not simplify or expand any expressions unless indicated. Note: the first step has been done for you and is the statement for n = k. The second step should be the equation that results when n is replaced by k+1. 17 + 35 + 53 + . . . +(18k -1) = k(9k + 8) 17 + 35 + 53 + . . . + (18k - 1) + The next step has been done for you and involves writing the equation that results after simplifying the expression in the box on the left side and grouping the remaining terms. Then after noticing that the grouped expression is the same as left side of the equation for n = k, replace the grouped expression with the right side of the equation for n = k and simplify second factor of the other side of the equation. 17 + 35 + 53 + . . . + (18k -1)+ 18k + 17 ? (k + 1)[9(k +1)+ 8] 0 +18k + 17 ? (k + 1)( +[) Now simplify the left side and then factor it. OK2 + Jk + ? (k+ 1)(9k+ 17) (K + 1) +) ? (K+1)(9k+ 17) You have just shown that the left and right sides of the equation that results from replacing n with k+1 are exactly equal (in other words, the statement is true for n = k+1) . Therefore, what is the next step in the induction proof? O A. The statement is not true for n = k + 1, given that it is true for n = k. We have disproved this statement by the Principle of Mathematical Induction. O B. The statement is true for n = k + 1, given that it is true for n = k. Since the statement is also true for n = 1, conclude by the Principle of Mathematical Induction that the statement is true for all natural numbers, n. Ask my instructor Print Media Clear all Check answe DEC 5 .... A W